/******************************************************************************
 * Copyright (C) 2014-2020 Zhifeng Gong <gozfree@163.com>
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 ******************************************************************************/
/*
 * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
 *
 *  1) A node is either red or black
 *  2) The root is black
 *  3) All leaves (NULL) are black
 *  4) Both children of every red node are black
 *  5) Every simple path from root to leaves contains the same number
 *     of black nodes.
 *
 *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
 *  consecutive red nodes in a path and every red node is therefore followed by
 *  a black. So if B is the number of black nodes on every simple path (as per
 *  5), then the longest possible path due to 4 is 2B.
 *
 *  We shall indicate color with case, where black nodes are uppercase and red
 *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
 *  parentheses and have some accompanying text comment.
 */
#include <stdio.h>
#include <stdlib.h>
#include "librbtree.h"

#define RB_RED      0
#define RB_BLACK    1

#define __rb_parent(pc)    ((struct rb_node *)(pc & ~3))

#define __rb_color(pc)     ((pc) & 1)
#define __rb_is_black(pc)  __rb_color(pc)
#define __rb_is_red(pc)    (!__rb_color(pc))
#define rb_color(rb)       __rb_color((rb)->__rb_parent_color)
#define rb_is_red(rb)      __rb_is_red((rb)->__rb_parent_color)
#define rb_is_black(rb)    __rb_is_black((rb)->__rb_parent_color)

static inline void rb_set_black(struct rb_node *rb)
{
    rb->__rb_parent_color |= RB_BLACK;
}

static inline struct rb_node *rb_red_parent(struct rb_node *red)
{
    return (struct rb_node *)red->__rb_parent_color;
}

static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
{
    rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
}

static inline void rb_set_parent_color(struct rb_node *rb,
                struct rb_node *p, int color)
{
    rb->__rb_parent_color = (unsigned long)p | color;
}

static inline void
__rb_change_child(struct rb_node *old, struct rb_node *_new,
                struct rb_node *parent, struct rb_root *root)
{
    if (parent) {
        if (parent->rb_left == old)
            parent->rb_left = _new;
        else
            parent->rb_right = _new;
    } else
        root->rb_node = _new;
}

/*
 * Helper function for rotations:
 * - old's parent and color get assigned to new
 * - old gets assigned new as a parent and 'color' as a color.
 */
static inline void
__rb_rotate_set_parents(struct rb_node *old, struct rb_node *_new,
                struct rb_root *root, int color)
{
    struct rb_node *parent = rb_parent(old);
    _new->__rb_parent_color = old->__rb_parent_color;
    rb_set_parent_color(old, _new, color);
    __rb_change_child(old, _new, parent, root);
}

#ifdef __ANDROID__
static void
#else
static __always_inline void
#endif
__rb_insert(struct rb_node *node, struct rb_root *root,
    void (*augment_rotate)(struct rb_node *old, struct rb_node *_new))
{
    struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;

    while (1) {
        /*
         * Loop invariant: node is red
         *
         * If there is a black parent, we are done.
         * Otherwise, take some corrective action as we don't
         * want a red root or two consecutive red nodes.
         */
        if (!parent) {
            rb_set_parent_color(node, NULL, RB_BLACK);
            break;
        } else if (rb_is_black(parent))
            break;

        gparent = rb_red_parent(parent);

        tmp = gparent->rb_right;
        if (parent != tmp) {    /* parent == gparent->rb_left */
            if (tmp && rb_is_red(tmp)) {
                /*
                 * Case 1 - color flips
                 *
                 *       G            g
                 *      / \          / \
                 *     p   u  -->   P   U
                 *    /            /
                 *   n            N
                 *
                 * However, since g's parent might be red, and
                 * 4) does not allow this, we need to recurse
                 * at g.
                 */
                rb_set_parent_color(tmp, gparent, RB_BLACK);
                rb_set_parent_color(parent, gparent, RB_BLACK);
                node = gparent;
                parent = rb_parent(node);
                rb_set_parent_color(node, parent, RB_RED);
                continue;
            }

            tmp = parent->rb_right;
            if (node == tmp) {
                /*
                 * Case 2 - left rotate at parent
                 *
                 *      G             G
                 *     / \           / \
                 *    p   U  -->    n   U
                 *     \           /
                 *      n         p
                 *
                 * This still leaves us in violation of 4), the
                 * continuation into Case 3 will fix that.
                 */
                parent->rb_right = tmp = node->rb_left;
                node->rb_left = parent;
                if (tmp)
                    rb_set_parent_color(tmp, parent,
                                    RB_BLACK);
                rb_set_parent_color(parent, node, RB_RED);
                augment_rotate(parent, node);
                parent = node;
                tmp = node->rb_right;
            }

            /*
             * Case 3 - right rotate at gparent
             *
             *        G           P
             *       / \         / \
             *      p   U  -->  n   g
             *     /                 \
             *    n                   U
             */
            gparent->rb_left = tmp;  /* == parent->rb_right */
            parent->rb_right = gparent;
            if (tmp)
                rb_set_parent_color(tmp, gparent, RB_BLACK);
            __rb_rotate_set_parents(gparent, parent, root, RB_RED);
            augment_rotate(gparent, parent);
            break;
        } else {
            tmp = gparent->rb_left;
            if (tmp && rb_is_red(tmp)) {
                /* Case 1 - color flips */
                rb_set_parent_color(tmp, gparent, RB_BLACK);
                rb_set_parent_color(parent, gparent, RB_BLACK);
                node = gparent;
                parent = rb_parent(node);
                rb_set_parent_color(node, parent, RB_RED);
                continue;
            }

            tmp = parent->rb_left;
            if (node == tmp) {
                /* Case 2 - right rotate at parent */
                parent->rb_left = tmp = node->rb_right;
                node->rb_right = parent;
                if (tmp)
                    rb_set_parent_color(tmp, parent,
                                    RB_BLACK);
                rb_set_parent_color(parent, node, RB_RED);
                augment_rotate(parent, node);
                parent = node;
                tmp = node->rb_left;
            }

            /* Case 3 - left rotate at gparent */
            gparent->rb_right = tmp;  /* == parent->rb_left */
            parent->rb_left = gparent;
            if (tmp)
                rb_set_parent_color(tmp, gparent, RB_BLACK);
            __rb_rotate_set_parents(gparent, parent, root, RB_RED);
            augment_rotate(gparent, parent);
            break;
        }
    }
}

/*
 * Inline version for rb_erase() use - we want to be able to inline
 * and eliminate the dummy_rotate callback there
 */
#ifdef __ANDROID__
static void
#else
static __always_inline void
#endif
____rb_erase_color(struct rb_node *parent, struct rb_root *root,
    void (*augment_rotate)(struct rb_node *old, struct rb_node *_new))
{
    struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;

    while (1) {
        /*
         * Loop invariants:
         * - node is black (or NULL on first iteration)
         * - node is not the root (parent is not NULL)
         * - All leaf paths going through parent and node have a
         *   black node count that is 1 lower than other leaf paths.
         */
        sibling = parent->rb_right;
        if (node != sibling) {  /* node == parent->rb_left */
            if (rb_is_red(sibling)) {
                /*
                 * Case 1 - left rotate at parent
                 *
                 *     P               S
                 *    / \             / \
                 *   N   s    -->    p   Sr
                 *      / \         / \
                 *     Sl  Sr      N   Sl
                 */
                parent->rb_right = tmp1 = sibling->rb_left;
                sibling->rb_left = parent;
                rb_set_parent_color(tmp1, parent, RB_BLACK);
                __rb_rotate_set_parents(parent, sibling, root,
                                RB_RED);
                augment_rotate(parent, sibling);
                sibling = tmp1;
            }
            tmp1 = sibling->rb_right;
            if (!tmp1 || rb_is_black(tmp1)) {
                tmp2 = sibling->rb_left;
                if (!tmp2 || rb_is_black(tmp2)) {
                    /*
                     * Case 2 - sibling color flip
                     * (p could be either color here)
                     *
                     *    (p)           (p)
                     *    / \           / \
                     *   N   S    -->  N   s
                     *      / \           / \
                     *     Sl  Sr        Sl  Sr
                     *
                     * This leaves us violating 5) which
                     * can be fixed by flipping p to black
                     * if it was red, or by recursing at p.
                     * p is red when coming from Case 1.
                     */
                    rb_set_parent_color(sibling, parent,
                                    RB_RED);
                    if (rb_is_red(parent))
                        rb_set_black(parent);
                    else {
                        node = parent;
                        parent = rb_parent(node);
                        if (parent)
                            continue;
                    }
                    break;
                }
                /*
                 * Case 3 - right rotate at sibling
                 * (p could be either color here)
                 *
                 *   (p)           (p)
                 *   / \           / \
                 *  N   S    -->  N   Sl
                 *     / \             \
                 *    sl  Sr            s
                 *                       \
                 *                        Sr
                 */
                sibling->rb_left = tmp1 = tmp2->rb_right;
                tmp2->rb_right = sibling;
                parent->rb_right = tmp2;
                if (tmp1)
                    rb_set_parent_color(tmp1, sibling,
                                    RB_BLACK);
                augment_rotate(sibling, tmp2);
                tmp1 = sibling;
                sibling = tmp2;
            }
            /*
             * Case 4 - left rotate at parent + color flips
             * (p and sl could be either color here.
             *  After rotation, p becomes black, s acquires
             *  p's color, and sl keeps its color)
             *
             *      (p)             (s)
             *      / \             / \
             *     N   S     -->   P   Sr
             *        / \         / \
             *      (sl) sr      N  (sl)
             */
            parent->rb_right = tmp2 = sibling->rb_left;
            sibling->rb_left = parent;
            rb_set_parent_color(tmp1, sibling, RB_BLACK);
            if (tmp2)
                rb_set_parent(tmp2, parent);
            __rb_rotate_set_parents(parent, sibling, root,
                            RB_BLACK);
            augment_rotate(parent, sibling);
            break;
        } else {
            sibling = parent->rb_left;
            if (rb_is_red(sibling)) {
                /* Case 1 - right rotate at parent */
                parent->rb_left = tmp1 = sibling->rb_right;
                sibling->rb_right = parent;
                rb_set_parent_color(tmp1, parent, RB_BLACK);
                __rb_rotate_set_parents(parent, sibling, root,
                                RB_RED);
                augment_rotate(parent, sibling);
                sibling = tmp1;
            }
            tmp1 = sibling->rb_left;
            if (!tmp1 || rb_is_black(tmp1)) {
                tmp2 = sibling->rb_right;
                if (!tmp2 || rb_is_black(tmp2)) {
                    /* Case 2 - sibling color flip */
                    rb_set_parent_color(sibling, parent,
                                    RB_RED);
                    if (rb_is_red(parent))
                        rb_set_black(parent);
                    else {
                        node = parent;
                        parent = rb_parent(node);
                        if (parent)
                            continue;
                    }
                    break;
                }
                /* Case 3 - right rotate at sibling */
                sibling->rb_right = tmp1 = tmp2->rb_left;
                tmp2->rb_left = sibling;
                parent->rb_left = tmp2;
                if (tmp1)
                    rb_set_parent_color(tmp1, sibling,
                                    RB_BLACK);
                augment_rotate(sibling, tmp2);
                tmp1 = sibling;
                sibling = tmp2;
            }
            /* Case 4 - left rotate at parent + color flips */
            parent->rb_left = tmp2 = sibling->rb_right;
            sibling->rb_right = parent;
            rb_set_parent_color(tmp1, sibling, RB_BLACK);
            if (tmp2)
                rb_set_parent(tmp2, parent);
            __rb_rotate_set_parents(parent, sibling, root,
                            RB_BLACK);
            augment_rotate(parent, sibling);
            break;
        }
    }
}

/*
 * Non-augmented rbtree manipulation functions.
 *
 * We use dummy augmented callbacks here, and have the compiler optimize them
 * out of the rb_insert_color() and rb_erase() function definitions.
 */

static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
static inline void dummy_copy(struct rb_node *old, struct rb_node *_new) {}
static inline void dummy_rotate(struct rb_node *old, struct rb_node *_new) {}

struct rb_augment_callbacks {
    void (*propagate)(struct rb_node *node, struct rb_node *stop);
    void (*copy)(struct rb_node *old, struct rb_node *_new);
    void (*rotate)(struct rb_node *old, struct rb_node *_new);
};

static const struct rb_augment_callbacks dummy_callbacks = {
    dummy_propagate, dummy_copy, dummy_rotate
};

void rb_insert_color(struct rb_node *node, struct rb_root *root)
{
    __rb_insert(node, root, dummy_rotate);
}

#ifdef __ANDROID__
static struct rb_node *
#else
static __always_inline struct rb_node *
#endif
__rb_erase_augmented(struct rb_node *node, struct rb_root *root,
                const struct rb_augment_callbacks *augment)
{
    struct rb_node *child = node->rb_right, *tmp = node->rb_left;
    struct rb_node *parent, *rebalance;
    unsigned long pc;

    if (!tmp) {
        /*
         * Case 1: node to erase has no more than 1 child (easy!)
         *
         * Note that if there is one child it must be red due to 5)
         * and node must be black due to 4). We adjust colors locally
         * so as to bypass __rb_erase_color() later on.
         */
        pc = node->__rb_parent_color;
        parent = __rb_parent(pc);
        __rb_change_child(node, child, parent, root);
        if (child) {
            child->__rb_parent_color = pc;
            rebalance = NULL;
        } else
            rebalance = __rb_is_black(pc) ? parent : NULL;
        tmp = parent;
    } else if (!child) {
        /* Still case 1, but this time the child is node->rb_left */
        tmp->__rb_parent_color = pc = node->__rb_parent_color;
        parent = __rb_parent(pc);
        __rb_change_child(node, tmp, parent, root);
        rebalance = NULL;
        tmp = parent;
    } else {
        struct rb_node *successor = child, *child2;
        tmp = child->rb_left;
        if (!tmp) {
            /*
             * Case 2: node's successor is its right child
             *
             *    (n)          (s)
             *    / \          / \
             *  (x) (s)  ->  (x) (c)
             *        \
             *        (c)
             */
             parent = successor;
             child2 = successor->rb_right;
             augment->copy(node, successor);
        } else {
            /*
             * Case 3: node's successor is leftmost under
             * node's right child subtree
             *
             *    (n)          (s)
             *    / \          / \
             *  (x) (y)  ->  (x) (y)
             *      /            /
             *    (p)          (p)
             *    /            /
             *  (s)          (c)
             *    \
             *    (c)
             */
            do {
                parent = successor;
                successor = tmp;
                tmp = tmp->rb_left;
            } while (tmp);
            parent->rb_left = child2 = successor->rb_right;
            successor->rb_right = child;
            rb_set_parent(child, successor);
            augment->copy(node, successor);
            augment->propagate(parent, successor);
        }

        successor->rb_left = tmp = node->rb_left;
        rb_set_parent(tmp, successor);

        pc = node->__rb_parent_color;
        tmp = __rb_parent(pc);
        __rb_change_child(node, successor, tmp, root);
        if (child2) {
            successor->__rb_parent_color = pc;
            rb_set_parent_color(child2, parent, RB_BLACK);
            rebalance = NULL;
        } else {
            unsigned long pc2 = successor->__rb_parent_color;
            successor->__rb_parent_color = pc;
            rebalance = __rb_is_black(pc2) ? parent : NULL;
        }
        tmp = successor;
    }

    augment->propagate(tmp, NULL);
    return rebalance;
}
void rb_erase(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *rebalance;
    rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
    if (rebalance)
        ____rb_erase_color(rebalance, root, dummy_rotate);
}

/*
 * This function returns the first node (in sort order) of the tree.
 */
struct rb_node *rb_first(const struct rb_root *root)
{
    struct rb_node *n;

    n = root->rb_node;
    if (!n)
        return NULL;
    while (n->rb_left)
        n = n->rb_left;
    return n;
}

struct rb_node *rb_last(const struct rb_root *root)
{
    struct rb_node *n;

    n = root->rb_node;
    if (!n)
        return NULL;
    while (n->rb_right)
        n = n->rb_right;
    return n;
}

struct rb_node *rb_next(const struct rb_node *node)
{
    struct rb_node *parent;

    if (RB_EMPTY_NODE(node))
        return NULL;

    /*
     * If we have a right-hand child, go down and then left as far
     * as we can.
     */
    if (node->rb_right) {
        node = node->rb_right;
        while (node->rb_left)
            node=node->rb_left;
        return (struct rb_node *)node;
    }

    /*
     * No right-hand children. Everything down and left is smaller than us,
     * so any 'next' node must be in the general direction of our parent.
     * Go up the tree; any time the ancestor is a right-hand child of its
     * parent, keep going up. First time it's a left-hand child of its
     * parent, said parent is our 'next' node.
     */
    while ((parent = rb_parent(node)) && node == parent->rb_right)
        node = parent;

    return parent;
}

struct rb_node *rb_prev(const struct rb_node *node)
{
    struct rb_node *parent;

    if (RB_EMPTY_NODE(node))
        return NULL;

    /*
     * If we have a left-hand child, go down and then right as far
     * as we can.
     */
    if (node->rb_left) {
        node = node->rb_left;
        while (node->rb_right)
            node=node->rb_right;
        return (struct rb_node *)node;
    }

    /*
     * No left-hand children. Go up till we find an ancestor which
     * is a right-hand child of its parent.
     */
    while ((parent = rb_parent(node)) && node == parent->rb_left)
        node = parent;

    return parent;
}

void rb_replace_node(struct rb_node *victim, struct rb_node *_new,
                struct rb_root *root)
{
    struct rb_node *parent = rb_parent(victim);

    /* Set the surrounding nodes to point to the replacement */
    __rb_change_child(victim, _new, parent, root);
    if (victim->rb_left)
        rb_set_parent(victim->rb_left, _new);
    if (victim->rb_right)
        rb_set_parent(victim->rb_right, _new);

    /* Copy the pointers/colour from the victim to the replacement */
    *_new = *victim;
}

static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
{
    for (;;) {
        if (node->rb_left)
            node = node->rb_left;
        else if (node->rb_right)
            node = node->rb_right;
        else
            return (struct rb_node *)node;
    }
}

struct rb_node *rb_next_postorder(const struct rb_node *node)
{
    const struct rb_node *parent;
    if (!node)
        return NULL;
    parent = rb_parent(node);

    /* If we're sitting on node, we've already seen our children */
    if (parent && node == parent->rb_left && parent->rb_right) {
        /* If we are the parent's left node, go to the parent's right
         * node then all the way down to the left */
        return rb_left_deepest_node(parent->rb_right);
    } else
        /* Otherwise we are the parent's right node, and the parent
        * should be next */
        return (struct rb_node *)parent;
}

struct rb_node *rb_first_postorder(const struct rb_root *root)
{
    if (!root->rb_node)
        return NULL;

    return rb_left_deepest_node(root->rb_node);
}
